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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-dvdemo2 | Structured version Visualization version GIF version |
Description: Remove dependency on ax-13 2392 from dvdemo2 5053 (this removal is noteworthy since dvdemo1 5052 and dvdemo2 5053 illustrate the phenomenon of bundling). (Contributed by BJ, 16-Jul-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-dvdemo2 | ⊢ ∃𝑥(𝑥 = 𝑦 → 𝑧 ∈ 𝑥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-el 33125 | . 2 ⊢ ∃𝑥 𝑧 ∈ 𝑥 | |
2 | ax-1 6 | . 2 ⊢ (𝑧 ∈ 𝑥 → (𝑥 = 𝑦 → 𝑧 ∈ 𝑥)) | |
3 | 1, 2 | eximii 1913 | 1 ⊢ ∃𝑥(𝑥 = 𝑦 → 𝑧 ∈ 𝑥) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1853 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1871 ax-4 1886 ax-5 1989 ax-6 2055 ax-7 2091 ax-8 2142 ax-9 2149 ax-10 2169 ax-11 2184 ax-12 2197 ax-pow 4993 |
This theorem depends on definitions: df-bi 197 df-an 385 df-ex 1854 df-nf 1859 |
This theorem is referenced by: (None) |
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